The Tropical Limit of String Theory and Feynman Integrals

Explore the fascinating intersection of string theory, Feynman integrals, and tropical geometry in this comprehensive lecture. Delve into the physics background, including Feynman rules and string diagrams, before examining the tropical limit of string theory. Discover tropical graphs, moduli spaces, and their applications to string amplitudes. Learn about the field theory limit and its implications for tree-level calculations. Conclude with a discussion of open questions in this cutting-edge area of theoretical physics and mathematics. Gain insights into the connections between combinatorial algebraic geometry, tropical geometry, and quantum field theory through this advanced presentation by Piotr Tourkine at the International Centre for Theoretical Sciences.

Syllabus

The Tropical Limit of String Theory and Feynman Integrals
Combinatorial Algebraic Geometry: Tropical and Real hybrid
Plan
I. Introduction - Physics background
Feyman rules
Remarks
Schematically
String diagram
String diagram at given loop order
String amplitude: genus expansion
Preview of results
Original goal
Problem of highly technical nature
II. The tropical limit of string theory
Tropical graphs
Examples
Tropical moduli space
Examples
Other examples
Dual graph
One central idea
Tropical Homology
Bosonic string amplitudes
Explicit construction
Field theory limit
Example @ tree - level
IV. A few open questions
Wrap Up